3) Consider a positive charge in a region of uniform electric field. If the charge moves in the direction of the field, is the potential energy increasing or decreasing? Is the field doing positive or negative work on the charge? 4. Three identical positive point charges of charge +Q are initially at rest at infinite separation. What is the potential energy needed to bring the charges at the corners of an equilateral triangle of sice length a? 5. Two charges of equal charge magnitude are separated by a distance d. Which of the following pairs of charge signs will lead to a zero electric potential at d/2 relative to in finity? 1. Both are positive 11. Both are negative Ill. Opposite signs

Force on a chaged particle in an electric field E is = Q E, where Q is charge on the particle.

Step-by-step explanation

a) Potential energy stored is given by F. dr where dr is small displacement.

If dr is in direction of force then potential will be negative, if dr is in opposite direction potential will be positive.

Here charge is moving in the field direction so potential will be negative (decreasing) and hence work done by field is negative.

b) To solve this first calculate all the forces required and then put it in  V= - F. dr    1   formula to get potentail energy formula.

for placement of first charge no force is requires as there is no other charge to attract or repel, for second charge we have to apply a force F= k Q /r² to place it (where r=a here) and for last chage we have to apply a force which is equal to resultant of force applied by previous two charges i.e. (F² + F² + 2F² cos60)^1/2 = 2F²(1+cos60)^1/2

now add all forces and put in 1 in place of F to get V.

c) So if both the charges at a distance have same sign i.e. either positive or negative then net force at d/2 will be 0 and hence by formula   V= - F. dr we have V=0.